Integer dependence in continuous function rings associated to compactifications
by
M. Ángeles Mulero
Univ. Extremadura, Badajoz,
Coauthors: Jesús M. Domínguez (Universidad de Valladolid)

Let X be a locally compact, noncompact Hausdorff space. We shall denote by C(X) the ring of all continuous real-valued functions on X. If Y and the embedding i:X --> Y is a compactification of X, then C(Y) can be seen as the subring of C(X) consisting of those functions that have continuous extension to Y. Let us now assume that Z, with the embedding j:X --> Z is another compactification of X, and such that there is a continuous map p: Z --> Y such that p o j=i. So that, C(Y) can be seen a subring of C(Z). This work deals with algebraic properties of this ring extension. We shall study when is this ring extension simple, that is, when does there exist a function f in C(Z) such that C(Z)=C(Y)[f]. This question was posed by G.D. Faulkner.

Date received: March 2, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafw-55.